Bioinformatics, 31(16), 2015, 2705–2712
doi: 10.1093/bioinformatics/btv216
Advance Access Publication Date: 21 April 2015
Original Paper
Systems biology
Analysis of impedance-based cellular
growth assays
Franziska Witzel1,2,4, Raphaela Fritsche-Guenther3, Nadine Lehmann1,4,
Anja Sieber1,4 and Nils Blüthgen1,2,4,*
1
Institute for Pathology, Charité Universitätsmedizin Berlin, 10117 Berlin, 2Institute of Theoretical Biology,
Humboldt-Universität zu Berlin, 10115 Berlin, 3BIMSB, Max-Delbrück-Centrum für Molekulare Medizin, 13092
Berlin and 4Integrative Research Institute Life Sciences, Humboldt-Universität zu Berlin, 10099 Berlin, Germany
*To whom correspondence should be addressed.
Associate Editor: Jonathan Wren
Received on December 23, 2014; revised on March 27, 2015; accepted on April 14, 2015
Abstract
Motivation: Impedance-based technologies are advancing methods for measuring proliferation of
adherent cell cultures non-invasively and in real time. The analysis of the resulting data has so far
been hampered by inappropriate computational methods and the lack of systematic data to evaluate the characteristics of the assay.
Results: We used a commercially available system for impedance-based growth measurement
(xCELLigence) and compared the reported cell index with data from microscopy. We found that the
measured signal correlates linearly with the cell number throughout the time of an experiment
with sufficient accuracy in subconfluent cell cultures. The resulting growth curves for various colon
cancer cells could be well described with the empirical Richards growth model, which allows for
extracting quantitative parameters (such as characteristic cycle times). We found that frequently
used readouts like the cell index at a specific time or the area under the growth curve cannot be
used to faithfully characterize growth inhibition. We propose to calculate the average growth rate
of selected time intervals to accurately estimate time-dependent IC50 values of drugs from growth
curves.
Contact: [email protected]
Supplementary information: Supplementary data are available at Bioinformatics online.
1 Introduction
Cell proliferation assays in multiwell format have become one of the
main workhorses in drug characterization and are used for cellular
phenotyping (Basu et al., 2013; Garnett et al., 2012). Screening of
thousands of compounds from drug libraries requires very costefficient approaches. Classical proliferation assays like the MTT or
XTT assay have a number of disadvantages. They are often not very
quantitative and are typically invasive, as they require labels which
influence cellular metabolism. Since culturing of the cells and application of the assay is the most laborious task, typically the assay is
performed only at a few time points after application of the
drug. Consequently, these assays may miss important kinetic
information.
Targeted therapies and ab initio design of novel kinase inhibitors
require more quantitative evaluation of drug effects on cell phenotype. Kinase inhibitors typically have nontrivial pharmacodynamics
that depends crucially on cell type and mutation pattern. Thus, it is
desired to record growth curves non-invasively and with high temporal resolution. Such a method for studying cellular processes in
real time was developed in the 1980s and became known as electric
cell-substrate impedance sensing (ECIS) (Giaever and Keese, 1993).
In this assay, the cell culture well bottom contains electrodes, typically a large reference electrode and one or several detection electrodes. Via these electrodes, a small alternating potential is applied,
and the impedance of the circuit is measured. Cells that grow on the
C The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: [email protected]
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detection electrodes increase the measured impedance, thus the
impedance should correlate with the number of cells. This method
has also been successfully used to study electric properties of the cell
membrane, the mode of cell attachment to the ground substrate as
well as cell motility (Giaever and Keese, 1991, 1993) and to analyze
cytotoxicity (Xiao and Luong, 2003; Xiao et al., 2002). Solly et al.
(2004) developed an assay called real-time cell electronic sensing,
which is based on ECIS; however, the electrode structure has
been improved to allow detection of almost all cells in a culture
well. Assay plates are now commercially available in multiwell
format.
In this study, we investigated how to improve the analysis of
growth curves measured by the assays. First, we compared cell index
data obtained by the assay with data on % confluency from microscopy. The analysis shows that the assay can be used to study proliferation quantitatively, as the measured cell index relates linearly to
the cell surface of adherent colon carcinoma cell lines. Next we evaluated if mathematical models can be used to describe the timeresolved measurements. We found that after seeding, adherent cells
require a certain time to attach to the surface, after which they start
to grow exponentially. The duration of the exponential growth
phase depends critically on initial cell number and the culture well
capacity, as increasing relative confluency will lead to contact inhibition of growth. After evaluating different growth models, we concluded that the different phases of the cell growth (after cell
attachment) can be appropriately described by the Richards growth
model (Richards, 1959). Parameters obtained from the model fit can
be used to derive quantities that characterize cell growth, such as the
doubling time of proliferating cells.
Besides, growth measurements are often used to determine quantitative traits of drugs, such as IC50 values. We found that the cell
index, the normalized cell index or the area under the growth curve
are error-prone readouts for quantification of growth. In contrast,
growth can be quantified reliably by calculating average growth
rates, and consequently these rates (when obtained from different inhibitor treatments) are suitable for IC50 estimation. Accurate timedependent IC50 values can be obtained by sampling the average
growth rate within several user-defined time intervals.
From our studies, we conclude that the technology is well suited
to quantify cell growth. However, the currently applied techniques
of growth curve analysis (such as the ones build into the software of
commercial systems) are insufficient for extracting quantitative information. In this work, we present quantitative computational
methods that make use of the dynamic information.
F.Witzel et al.
2.2 Reagents
The following inhibitors were used in the growth assays: Mek
inhibitor U0126 (Promega), Raf inhibitor Sorafenib (LC
Laboratories), PI3K inhibitor LY294002 (Axxora Deutschland) and
the EGFR inhibitor Erbitux (Charité Universitätsmedizin Berlin).
The solvent control was DMSO (used in the same concentration as
in solutions that contain an inhibitor).
2.3 Growth measurement
Real-time analysis of proliferation was performed using the
xCELLigence system RTCA SP from ACEA Biosciences. Cells are
grown in the disposable E-Plate 96, a microtiter plate with gold electrode structures of biocompatible surface at the bottom of each well.
Electrode and respective counter electrode have a complex interdigitated structure (as shown in Fig. 1A) and both combined cover 80%
of the ground. The RTCA device measures the impedance at an
alternating voltage of 20 mV and 10 kHz frequency. As the whole
device is housed inside of an incubator, the cells are kept at optimal
culture conditions (5% CO2, 37 C) during the measurement. The
growth assay was performed according to the instructions of the
manufacturer.
2.4 Image analysis
To observe cells in the xCELLigence system, we used the E-Plate
VIEW 96, where four rows of electrode structures have been left
out, yielding an electrode surface coverage of 70%. Bright field
images of the cells were segmented automatically using functions of
the Image Processing Toolbox of MATLAB. Briefly, the gold electrode structures, which appear as well-defined dark objects in the
pictures, were detected by k-means clustering of the luminosity layer
and removed from the images thereafter. Cells were detected using
texture segmentation, i.e. by applying a range filter that amplifies intensity variations in the neighborhood of an image pixel. We calculate confluency by counting total image pixels and pixels that make
up the segmented areas.
2.5 IC50 estimation
We compare four different readouts for quantification of cell
growth. These readouts are the cell index ci, the normalized cell
index ci=ciðtref Þ, the area under the curve and the average growth
rate log ½ci=ciðtref Þ, where tref refers to a reference time point. We
normalized the quantities to the respective value of the control curve
(to obtain the relative inhibition Inhrel ) and fitted the correlation
with the inhibitor concentration c to the Hill-slope model
2 Materials and Methods
Inhrel ¼ a þ
2.1 Cells and cell culture
Human colorectal cancer cell lines HCT116, RKO and HT29 were
obtained from ATCC (American Type Culture Collection, UK).
LIM1215 were kindly provided by Prof. John Mariadason (Ludwig
Institute for Cancer Research Austin Hospital, Melbourne,
Australia). HCT116, RKO and Lim1215 were maintained in
DMEM (Dulbecco‘s Modified Eagle‘s Medium, Lonza), supplemented with 10% fetal calf serum, 1% ultraglutamine and 1% penicillin/streptomycin. HT29 were maintained in L-15 (Leibovitz)
supplemented with 0.1% (w/v) NaHCO3, 4% (w/v) glucose, 0.2%
of 1.4 mg/ml insulin, 1% of 10 mM MEM vitamins (Biochrom AG),
0.5% of fetuin/transferrin solution (0.12%/0.05%) (w/v), 10% fetal
calf serum, 0.5% ultraglutamine and 1% penicillin/streptomycin.
All cells were incubated in a humidified atmosphere of 5% CO2 in
air at 37 C.
1a
c n
1 þ IC50
(1)
to obtain the parameters a (maximal relative inhibition), the steepness n and the IC50 value, using the lsqnonlin fitting routine of
MATLAB.
3 Results
3.1 Impedance measurement as a non-invasive method
to study proliferation of adherent cells
We first set out to investigate how well impedance measurements reflect the cell number of adherent cells. For this, we used a commercially available system (xCELLigence) (Ke et al., 2011). Essentially,
the instrument measures the impedance in a 96-well format. The system calculates a so-called cell index, which is proportional to the
Analysis of impedance-based cellular growth assays
A
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confluency %
Fig. 1. Cell index correlates with cell surface and reflects proliferation.
(A) Sketch of the electrode structures at the bottom of an E-Plate 96 well. An
electrode is characterized by a circle-on-line structure, where the arrays of
one electrode (shown in black) are interdigitated with the arrays of the counter electrode (shown in gray). (B) Automatic image segmentation is used to
find the borders of cells (indicated with white lines) that are growing in the
electrode structure free zone of the E-Plate VIEW 96. Analysis of correlation of
cell index and % confluency of RKO cells in (C–F) and of HT29 in (G–J).
Microscopic images showing proliferation (C,G) which correlates with
increasing cell index values in the corresponding growth curves in panels
(D) and (H). The curves are broken at times when the plate was removed for
microscopic analysis. The corresponding % confluency estimated from the
microscopic images is shown in the insets. The correlation of % confluency
(as estimated by automated image segmentation) and measured cell index
from 20 growth curves at four time points for each cell line, RKO and HT29, respectively, is resolved by the time point of analysis in panels (E) and (I) and by
the number of seeded cells in panels (F) and (J) (5k cells ¼ 5000 cells). The
Pearson correlation of all data is indicated with R. A significantly improved
linear correlation of a subgroup of the data is indicated with in the figure
legends. The dashed line in panel (E) indicates that data with relative confluency 80% also show improved linearity. For the statistical analysis of significance, refer to the Supplementary Section 1.2
impedance from which the background (i.e. impedance of the circuit
in presence of medium but without cells) is subtracted. This index
increases when the electrode structures become successively covered
with adherent cells. Thus, the cell index is not a direct function of
cell number, but rather of the collective cell surface, the mode of cell
attachment and cell membrane composition. Therefore, it is important to establish that the increase in the cell index is primarily due to
the formation of new adherent cells.
To experimentally determine if the cell index faithfully reports
cell numbers, we used 96-well plates in which the central four rows
of the electrode structures in each well were left out, allowing to inspect relative confluency using microscopy. In these plates, we
seeded either 5 103, 104 or 2 104 cells per well, which we either
left untreated (triplicates per cell line, HT29 and RKO) or treated
with Mek-inhibitor U0126 or its vehicle control DMSO (both in duplicates per cell line for cells seeded at 104 or 2 104 cells). Growth
curves were recorded over a time period of 4 days with daily interruptions for microscopic analysis to estimate % confluency.
Figure 1C and G shows examples of bright field images taken
from the electrode-free zone for untreated RKO (5 103 cells/well
initially) and HT29 (2 104 cells/well initially) at the indicated time
points. The corresponding growth curves are shown in Figure 1D
and H. To determine the relative confluency in an unbiased way, we
used automated image segmentation to find the borders of cells (as
shown in Fig. 1B) and counted the image pixels covered by cells.
The insets of Figure 1D and H show the % confluency that was estimated for RKO and HT29 cells from images in Figure 1C and G. In
independent experiments where we used life-cell imaging with nuclear markers, we established that the cell surface area is linearly
correlated with cell number for these cells (see Supplementary
Figs S1 and S2).
Next we related the relative confluency with the cell index.
Figure 1E,F and I,J show the results for RKO and HT29, respectively. There is a clear linear correlation of % confluency with cell
index for the cell line HT29 with a Pearson correlation coefficient of
0.93. For very high relative confluency (close to 100%), the curve
shows saturation. The reason for this is unclear. Estimation errors
may arise as we extrapolate cell % confluency of the whole well
from the small proportion of the well that is accessible for microscopy. Also, in a previous study, it was found that in general, the cell
index represents cell number only for sub-confluent cultures
(Solly et al., 2004). In line with this, we often observed significant
changes in the cell index even after the cells have reached confluency, which might reflect changes in the cells mode of attachment.
Consequently, impedance growth curves should not be evaluated
as proportional to cell number after the curve has approached a
plateau.
For RKO cells, we observed stronger deviations from linearity,
the Pearson correlation was 0.82 when all data points are taken into
account. Again, deviation resulted mainly from data at high % confluency, and linear correlation was significantly higher when only
data below a level of 80% confluency were taken into account (indicated with the dashed line in Fig. 1).
Visual inspection of the data shown in Figure 1F and J suggested
that correlation within the groups of cells seeded at the same density
is higher than overall correlation. The cell index seems to have
shifted to higher values in a systematic fashion with increasing numbers of seeded cells (subgroups with significantly improved correlation are marked with a star in Figure 1E, F, I and J, see
Supplementary Section 1.2 for the statistical analysis). One interpretation is that initial cell density influences the attachment mode
and thus also subsequent measurements of the cell index. These
2708
A
1)
k
G
2)
3)
C
3
2
data
exp. fit 1)
1
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# cells x
# cells x
B
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50 100
time [hours]
150
data
logistic fit 2)
1
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50 100
time [hours]
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E
D
# cells x
results suggest that generally assays should be started with the same
number of seeded cells to make them comparable.
Another parameter that could influence linearity is a change of
the properties of the growth medium over time. The measured impedance could be influenced by changes in temperature and pH of
the medium, which is acidified over time by the cellular metabolism.
Grouping the data by the time point of measurement, however, did
not lead to significant improvement in the linear correlation, except
for the 24 h subgroup of RKO cell data (Fig. 1E and I). Data of later
time points for RKO are rather characterized by a higher spread
which might be due to almost total confluency. However, there are
some more indications for an influence of the growth medium. For
instance, the impedance measured after each microscopic analysis is
reduced compared with the impedance measured before the plate
was removed (see growth curve of RKO cells in Fig. 1D). RKO cells
have been cultured in DMEM which has a bicarbonate buffer system
and thus heavily depends on the ambient CO2 concentration. When
wells that contained only medium were measured, the cell index
dropped constantly, both for DMEM and L-15 (see Supplementary
Fig. S3). Assuming that this effect contributes in a linear fashion to
the cell index, this would increase inaccuracies for later time points
of the measurement. We have reevaluated the correlation of % confluency with cell index after subtraction of medium curves and
found only slight improvements in linearity of % confluency and
cell index (Supplementary Fig. S3). However, it is beyond our scope
to estimate in which way the medium impedance contributes to the
total measured impedance. Medium changes during time-course experiments should be avoided as they perturb the correlation between
cell index and cell number. We conclude that the cell index reports
% confluency of RKO and HT29 cells with acceptable accuracy, as
long as the culture is sub-confluent and the experimenter seeds the
same amount of cells in each well. The % confluency also relates to
cell number, as long as the cells are far from confluency where their
contact surface might be significantly decreased.
F.Witzel et al.
3
2
data
Richards fit 3)
1
0
0.06
Logistic
0.04
Richards
0.02
Exponential
0
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50 100
time [hours]
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Fig. 2. Model selection. (A) The growth of adherent cells in confined space.
The growth rate constant k is determined by the speed of cell division. The
maximum cell index G is mainly the result of a limited surface for adherent
cell growth of a cell monolayer. The exponential (1) and the logistic growth
model (2), as well as the growth model according to Richards (3) are presented in their differential form. (B–D) The integrated form of the three different growth models (for integrated forms see Supplementary Table S4) was
fitted to the growth curve of RKO cells, which were seeded at a density of
100 cells/ll and left untreated. We draw in panel (E) how the relative growth
rate (h–1) changes over time as predicted from the three different model fits
3.2 Model-based analysis of growth curves
After having established that the cell index can be used as a linear
measure of cell number, we next aimed to describe the growth
curves using mathematical models. This offers the possibility to reliably estimate various factors like the cells’ characteristic growth
rate, contact inhibition and kinetics of drug action. We investigated
three models to describe cell growth with increasing model complexity. The simplest reasonable growth model is exponential growth,
which is the solution of a linear ordinary differential equation
(ODE) where growth is proportional to the cell number and the
growth rate k (ODE 1 in Fig. 2A). The second model has an additional parameter G that reflects the maximal capacity of the well,
and the growth rate decreases with cell number until G is reached
(ODE 2 in Fig. 2A). This model is known as the Logistic equation
(Verhulst, 1845) and was used to predict the population dynamics
of countries and has since then been successfully used in theoretical
ecology. The third model is a generalization of the logistic growth
model, the so-called Richards model (Richards, 1959) (ODE 3 in
Fig. 2A). In this model, an additional ‘shape’ parameter m changes
the sharpness in which growth rate is reduced. For m ¼ 2, the
Richards model coincides with the Logistic model, and with increasing m, the transition to lower growth rates is shifted to later time
points. None of the three models can describe the initial process
of cell attachment, and to compare the performance of the models
independent of this deficit, we omitted the data from the first 10 h.
Practically, however, parameter estimation is not influenced
by the omitted time interval and even performs similarly well
if the whole growth curve is used for fitting (see Supplementary
Fig. S4).
When fitting these three models to the experimental data, we
observed that both the simple exponential growth model and the
logistic equation do not faithfully describe the kinetics (see Fig. 2B
and C, respectively). In contrast, the Richards model fits the growth
curve with high quantitative accuracy (Fig. 2D). Figure 2E shows
schematically for these three models, how the growth rate dx
dt =x
changes over time. In the exponential model, the growth rate is constant, whereas the growth rate is steadily decreasing in the logistic
model. In contrast, the Richards model (for m > 2) has an extended
period with constant growth rate, which is followed by a rather fast
decline, similarly to what is seen in real growth rates. Accordingly,
the Richards model fits the first 100 h of the growth curve very well
(Fig. 2D), from which we can draw the conclusion that in this example the cells grow exponentially (with a constant rate) during the
first 60 h, before contact inhibition starts to reduce growth. After
about 100 h, the growth curve drops, which might be attributed to
advancing medium acidification, cell death due to consumption of
nutrients or detaching cells. The model presented here was not
intended to capture these processes, and thus data points at these
late time points need to be removed from the analysis. Although
simpler models systematically deviate from the growth curves, the
Richards model describes the data with reasonable accuracy.
Analysis of impedance-based cellular growth assays
RKO
2
data
fit
2
0
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100
time [hours]
150
0
50
100
time [hours]
150
cell index
0
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20.8 6 0.6 h
22.2 6 2 h
9.6 6 2.6 h
21.1 6 3.9 h
3.3 Using growth curves to characterize the effect of
small-molecule inhibitors
150
time [hours]
0
50
100
time [hours]
150
Fig. 3. Richards model fit. The Richards model can be used to fit the growth
curves of different sub-confluent colon cancer cell lines. The figure shows
one exemplary growth curve and the respective fit of the Richards model for
each cell line. Parameters of the fit are shown in the Supplementary Table S5
in the Supplementary Material
Most importantly, it is the only model that can describe the biphasic growth processes observed in all tested cell lines where an
extended exponential growth phase is followed by a rather short
phase of saturation (Fig. 2E). Also, the additional shape parameter
makes the Richards model much more flexible and applicable in a
general fashion than the logistic model.
From the parameters of the fitted Richards model, one can calculate the characteristic cell cycle time, by the following equation:
t2 ¼
Lim1215
2
0
0
HCT116
4
Lim1215
2
HT29
complicated growth curves (e.g. see Supplementary Fig. S8).
Constructing a model of higher complexity to account for that is
feasible; however, parameterization can become difficult. In the
next section, we outline how complex time-dependent inhibition
profiles can be evaluated without model fitting.
HCT116
4
RKO
Cycle times have been determined from the parameters of 12 independent
model fits (12 technical replicates for RKO and 12 replicates from 4 experiments for the other cell lines) according to formula (2). The respective growth
curves are shown in Supplementary Figure S5
0
0
cell index
Table 1. Cell cycle times of colon cancer cell lines
HT29
cell index
cell index
4
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m1
ln 2
k
(2)
This formula is based on the growth rate for small cell numbers
and thus represents a lower limit of the cell cycle time with zero contact inhibition. We used fits of the Richards model to datasets of
four different colon cancer cell lines to obtain estimates for the doubling time. Figure 3 shows representative model fits and Table 1
contains the estimated doubling times. Interestingly, they range
from just below 10 h (HCT116 cells) to 22 h (HT29 cells). The variability of the growth curves within an experiment is less pronounced
than between different experiments (see Supplementary Fig. S5 for
all growth curves the analysis is based on). The surprisingly short
doubling time of about 10 h in HCT116 cells is not an artifact of the
Richards model fitting procedure and can be confirmed when fitting
an exponential model to the period of the assay where the cells grow
with constant rate (Supplementary Fig. S6). We additionally estimated the cycle time from a live cell imaging experiment and obtained t2 ¼ 10.7 6 1.9 h, which compares with the impedance-based
result (details in Supplementary Fig. S7).
The Richards model is a flexible growth model for cells that
grow with a constant growth rate under the influence of contact inhibition. However, different phenomena like time-dependent inhibition or cell cycle synchronization of the cells might create more
Next we asked how the growth curves can be used to extract information about the action of small molecule inhibitors. As an example, we investigate how the inhibitor concentration of half
maximal inhibition, best known as the IC50 value, can be most reliably calculated from the growth curves. Often, the inhibitor affects
cell growth in a complex time-dependent manner, thus a modelbased analysis would depend crucially on the assumption about the
time profile of the inhibitor. Here we concentrate on estimating the
average effect of an inhibitor in a time interval, which is a typical
question in pharmacology. To benchmark different approaches, we
used datasets generated in silico using the Richards growth model,
in which we modeled the effect of the inhibitor by decreasing the
growth rate k according to the Hill-slope model [Equation (1), see
also (Sebaugh, 2011)] with half-maximal inhibition at IC50 ¼ 4 mM
(Fig. 4A).
Figure 4B shows the simulated growth curves for the set of
growth rates from Figure 4A. All curves start with the same initial
cell number or cell index. However, in experiments, the initial cell
index from different wells is subject to variations due to the pipetting error and differences in the number of cells that actually survive
and attach after seeding. As the initial phase of cell growth (after
cell attachment) is exponential, the error becomes more pronounced
after a few hours of growth. Typically, the cells are incubated for
24 h prior to inhibitor application, so that the spread in cell index
values amplifies during this period of time. Increased initial cell
number may lead to an apparent increase in growth rate, as the absolute increase of the cell index is larger for higher number of cells.
Figure 4C shows the influence of varying initial cell numbers. Here,
three growth curves have been calculated for a high growth rate
(representing control cells) and a low growth rate (representing inhibited cells), which differ by the initial cell index. One of the
growth curves with low k (upper dashed line) has a slightly higher
initial cell number, and it seems that growth is faster than in the
other two growth curves with the same k (other two dashed lines). It
shows that the cell index value at a given time point alone does not
help to reliably estimate growth.
To investigate how well different methods of IC50 estimation
perform in a realistic setting, we have generated 10 000 sets of
growth curves for six inhibitor concentrations with initial cell indices placed randomly between 0.2 and 0.4, reflecting the experimentally observed spread of cell index at 24 h after seeding. For all
10 000 sets, we have estimated the IC50 at 24, 48 and 72 h after inhibitor application, with four different methods: (i) the ci value at a
given time point, (ii) the area under the curve up to the time point,
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Fig. 4. The estimation of the IC50 value from growth curves. We use the model of Richards to simulate growth curves with increasing degree of inhibition, by
reducing the growth rate k while all other parameters are left unchanged. The various growth rates are related to different concentrations of the inhibitor according to the Hill-slope model with IC50 of 4 lM (A). The in silico growth curves resulting from the different growth rates from (A) are shown in (B). Slight variation of
the initial cell index mimics inhibition, which is illustrated in panel (C). We show theoretical triplicates of either a control growth curve (solid line) or a treated
growth curve (dashed line), respectively, where all parameters are identical, except for the initial cell index at t ¼ 0. Panel (D) shows how different ways of IC50
calculation perform, when we analyze growth curves with continuously decreasing growth rate as shown in panel (B); however, the initial cell index is randomly
varied on a cell index interval of [0.2,0.4]. The upper row shows the distribution of estimated IC50s from 10 000 trials, when they were either determined after
24 h, 48 h or 72 h (outliers of the distribution were omitted in this figure). The fit of relative inhibition versus inhibitor concentration [using Equation (1)] that leads
to the respective IC50 value is shown exemplary for one trial in the lower panel. The four different methods of IC50 calculation are described in the main text
(iii) the normalized ci value ci(t)/ci(t ¼ 0) of the time interval and (iv)
the logarithm of the normalized ci value for the time interval. The
distribution of the estimated IC50 values is shown in the upper panels of Figure 4D. The lower panels of the figure show one exemplary
fit (out of 10 000) of the respective quantity (normalized to the solvent control) versus concentration of the inhibitor using the Hillslope model Equation (1). The methods can be compared based on
two criteria: first, the ability of the method to identify the right IC50
of 4 mM and, second, the robustness of the estimator.
The simplest method is to calculate the IC50 from the cell index
value that is reached at a specific time, e.g. at 24 h. When applying
this method to the simulated data, resulting IC50 value estimations
varied strongly, spreading on an interval between close to 0 and
18 mM, and 50% being more than a factor of two away from the
real IC50 at 4mM (see left upper panel in Fig. 4D). After 48 h and
even more so after 72 h, the influence of the initial cell index spread
on the estimated IC50 is reduced; however, the median of the estimations deviates to lower IC50 values. Thus, this method biases the
estimate of the IC50 value. Another frequently used approach is to
calculate the IC50 based on the area under the growth curve (upper
panel, 2nd from left, Fig. 4D). As the area is proportional to the
arithmetic mean of the cell index, it is not surprising that it is also a
non-robust estimator with similar bias. Obviously, both methods
suffer from the influence of the initial cell index. Not surprisingly,
normalizing the cell index by the initial cell index reduces the spread
of the estimation (see upper panel, 2nd from right, Fig. 4D).
However, this estimator systematically underestimates the IC50.
This is primarily because the ratio of cells at different time points is
not proportional to the growth rate. Thus, we reasoned that for
near-exponential growth, the number of cell doublings within a time
window is the better measure. This quantity can be calculated by
taking the logarithm to the base 2 of the normalized cell index, as
shown in the upper right panel of Fig. 4D. Using this estimate, the
correct IC50 can be found independently of the initial cell index,
with very little uncertainty and no bias at early time points. The
logarithm of the normalized cell index is in accordance with an average growth rate, per definition. Consequently, this measure can be
used to reliably calculate IC50 values, over a time interval, in which
Analysis of impedance-based cellular growth assays
A 4
4
48h
2711
sc
0.1
1
36-48h
doublings
doublings
24-36h
24h
2
0
0
2
5
10
25
50
0
20 40 60 80
time [hours]
0
20 40 60 80
time [hours]
1
norm. growth rate
norm. growth rate
B
0.5
24h (19.7µM)
48h (15.7µM)
−2
0
10
10
c inhibitor [µM]
1
0.5
2
10
24-36h (5.7µM)
36-48h (25.7µM)
−2
0
10
10
c inhibitor [µM]
2
10
Fig. 5. Time-dependent IC50 of U0126 in HT29 cells. HT29 cells have been
treated with various concentrations of U0126 (concentrations in legend in
mM) ca. 20 h after seeding and sc is the solvent control DMSO. In (A), the solid
lines show the mean number of doublings since inhibitor application from
three replicates. The spread around the lines reaches from the minimum to
the maximum value of the replicates. The IC50 value of U0126 has been estimated over an interval of 24 h and 48 h after inhibitor application (left panel
in A) and over the time interval between 24 and 36 h or 36 and 48 h (right
panel in A). The corresponding fits of the Hill-slope model (1) with a ¼ 0 are
shown in panel (B). The legend indicates the time interval from which the
data have been taken and the respective estimated IC50 value in parentheses
the cells still grow exponentially. However, if the average growth
rate is calculated at 72 h, some cells are already contact inhibited
and grow slower not because of the inhibitor but due to this spatial
limitation. As a consequence, the growth rate of cells treated with
lower inhibitor concentrations approaches the growth rate of cells
treated with higher concentrations which are not contact inhibited
and it seems like the inhibitor is less effective, hence the IC50 value
becomes slightly overestimated (Fig. 4D upper right panel, at 72h).
We conclude that by using the average growth rate (or number of
cell doublings), the IC50 can be well estimated, without bias and
with little influence of initial spread of the cell index. The experimenter can choose the time interval ad libitum (e.g. the average
growth rate between 28 and 42 h). Thus, a time-dependent IC50
value can be generated by sampling different time intervals of the
growth curve. In this way, inhibitor kinetics may be revealed, even
when the time-dependent growth rate k(t) is not directly accessible.
Later time points of the growth assay cannot be analyzed, as contact
inhibition obscures the effect of a proliferation inhibitor.
Finally, we illustrate the average growth rate approach for IC50
estimation on the basis of a dataset of HT29 cells, which had been
treated with different concentrations of U0126 (triplicates per treatment). In Figure 5A, we show the growth curves in a transformed
version, as doubling events since 2 h after inhibitor application (our
reference time tref ). All cell index values (ci) of the curve are transformed according to
doublings ¼ log 2
ciðtÞ
:
ciðtref Þ
(3)
There are two advantages of this transformation. First, it enables
averaging over replicates. In this figure, each solid line represents the
mean of three replicates and the shade spreads from the minimum to
the maximum value of the replicates. The spread of the data is
greatly reduced compared with the presentation of raw cell index
values, which are influenced by the initial value (see Supplementary
Fig. S9 for a plot of the raw data). Second, the slope in these curves
is proportional to the growth rate. By comparing the slopes, it can
be said already by eye inspection, which cells grow faster than
others. In this experiment, we see time-dependent inhibition.
Between 24 and 36 h, cells that were treated with more than 10 mM
of U0126 are basically growth arrested (see right panel of Fig. 5A),
whereas growth restarts in the next 12 h. Accordingly, the IC50
value calculated based on the average growth rate between 24 and
36 h is almost 5-fold lower than the derived IC50 value based on the
next 12 h (see right panel of Fig. 5B). This effect is much less pronounced when the IC50 value is derived based on the average
growth rate of the first 24 h or 48 h after inhibitor application (left
panels of Fig. 5A and B).
This example shows that growth curves offer a wealth of information when it comes to the time-dependent effects of inhibitors
and that the time window chosen for analysis will influence what
properties can be extracted. Time intervals in which some treatment
leads to growth arrest are of general interest when characterizing inhibition kinetics.
4 Discussion and Conclusion
Use of impedance-based technologies to monitor various different
types of cells over time has become more popular in the last years,
and about 30% of recorded publications at Pubmed (search terms
xCELLigence AND proliferation) have been published in 2014.
These reports include proliferation studies on human cancer cell
lines (Caputo et al., 2014; Dowling et al., 2014; Módis et al., 2014);
however, the authors mostly restrict the data analysis to rather
qualitative descriptions.
The analysis of proliferation with the xCELLigence technology
crucially depends on the linear correlation of the cell index to the
cell number. Linearity has been shown for the cell index from
BALB/c 3T3 (Xing et al., 2006) and NIH 3T3 cells (Xing et al.,
2005) when they were seeded at different densities and measured 6 h
thereafter. We have exemplarily shown that the cell index faithfully
reports cell-covered area throughout the time course of 4 days, by
comparing the cell index with the total cell surface estimated by
microscopy.
We have found that the Richards growth model appropriately describes the growth curves of various colon cancer cell lines in the
xCELLigence system. In this model, exponential growth eventually
slows down most likely due to contact inhibition. However, the model
formulation is empirical—geometrical aspects of two dimensional cell
growth are ignored. In the extreme case where all cells are seeded in
one spot, contact inhibition takes effect immediately and virtually
only the cells at the border of the colony will still proliferate. The consequence would be a quadratic growth law instead of the expected exponential growth (Cherry and Papoutsakis, 1989). However, the
ability of cells to migrate might counteract the limitation of proliferation to cells at the border. The concerted effects of cell seeding patterns and cellular migration on proliferation have been studied with a
cellular automaton model (Lee et al., 1995). Surprisingly, at uniform
distribution of cells in the culture well, the stochastic simulation produces growth curves that show strong similarity to the Richards
growth model. As HT29 and RKO cells are characterized by rather
low basic migration rates, we conclude that the even distribution of
cells after seeding is the main reason for the observed initial period of
2712
exponential growth, where contact inhibition severely affects the
growth kinetics only close to confluency. This explains why the empirical and thus rather simple Richards model is perfectly suited for our
intentions. Because of its flexibility concerning the time course of
growth inhibition, it has been used widely to describe growth curves
(Tjørve and Tjørve, 2010). By fitting the model to the data, one can
determine the doubling times during the exponential growth phase at
total absence of contact inhibition.
Currently, one of the major usages of this technology is to compare growth under different conditions. For example, growth measurements using different concentrations of inhibitors are used to
estimate the IC50 value. However, we show that currently applied
techniques to extract quantitative parameters from the growth
curves are unreliable. Neither the area under the curve nor the slope
of a growth curve corresponds to the average growth rate. Though
the calculation of a normalized cell index creates robustness toward
fluctuations of the initial cell number, it is frequently and wrongly
believed that this parameter presents a proper measure of the growth
rate. We have shown that the logarithm of the normalized cell index
corresponds to the average growth rate of a time interval and this
measure also compensates for fluctuations of the initial cell index.
As a consequence, we do not recommend averaging over the raw
cell index values of replicates but to average the logarithm of the
normalized cell index.
Average growth rates, over time intervals of ad libitum choice, are
suited for calculation of time dependent IC50 values. The commercial
software that is shipped with the instrument (RTCA software, version
2.0 January 2013) offers the possibility to use either the raw cell index
values, the normalized cell index values or the area under the curve
for IC50 analysis—yet none of these quantities represent the degree of
inhibition in terms of the effect on the cells growth rate, rendering the
RTCA software insufficient for analysis of proliferation. Also in cytotoxicity assays, the logarithmic transformation of the data can be
beneficial for IC50 determination as apoptosis reflects an exponential
decay of the cell index. The calculation of average growth rates is not
recommended for migration or invasion assays as these processes may
not follow exponential kinetics.
Compared with conventional label-based proliferation assays,
impedance-based assays offer kinetic information while saving
working time. Experimental errors are reduced greatly, as the various time points are obtained from one and the same well, and small
pipetting errors between different wells can be compensated for by
evaluating average growth rates. On the other hand, the cell impedance is a complex quantity which depends on different cell parameters. It has been observed that a decrease in cell index is not always
associated with cytotoxicity, just like an increased cell index does
not have to reflect proliferation (Atienzar et al., 2011). Thus, we believe it remains essential to verify whether the measured increase of
the cell index faithfully represents proliferation. Given this condition
is fulfilled, we have shown how model fitting or the calculation of
average growth rates of defined time intervals can be used to really
benefit from the valuable kinetic information that impedance-based
proliferation assays provide.
F.Witzel et al.
Funding
This work was supported by the German Federal Ministry of Education and
Research through grants FORSYS and OncoPath.
Conflict of Interest: none declared.
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